Question: $f(n) = 6n^{2}+2(g(n))$ $g(t) = -5t^{2}-2(h(t))$ $h(t) = -7t-2$ $ g(h(-1)) = {?} $
Explanation: First, let's solve for the value of the inner function, $h(-1)$ . Then we'll know what to plug into the outer function. $h(-1) = (-7)(-1)-2$ $h(-1) = 5$ Now we know that $h(-1) = 5$ . Let's solve for $g(h(-1))$ , which is $g(5)$ $g(5) = -5(5^{2})-2(h(5))$ To solve for the value of $g$ , we need to solve for the value of $h(5)$ $h(5) = (-7)(5)-2$ $h(5) = -37$ That means $g(5) = -5(5^{2})+(-2)(-37)$ $g(5) = -51$